Reason is the ability to draw conclusions and foresee outcomes. It is sometimes called common sense. Science is reason squared: observations become data, and hypotheses are accepted as theory after being tested by repeated experiment. Using reason, humans associated disease with an invisible agency, which is why malaria has its name, from mal aria (bad air). Using science, humans grasped the fact that malaria was a microscopic infection delivered by an identifiable insect in particular climatic conditions, one that could be treated and prevented. Reason took humans as far as the Renaissance and a global population numbered in hundreds of millions, with a life expectation of perhaps 40 years. Science has doubled life expectancy, taken the global population towards 7 billion, and equipped almost 5 billion with mobile phones.

The question raised by Martin Rees, astronomer-royal and president of the Royal Society, in his Reith lectures – the last of which is broadcast on Radio 4 today – is whether humans are smart enough to make the best of the accelerating advance of science. Lord Rees's book, Our Final Century, speculates that human civilisation may not survive another 90 years. The cocktail of modern biology and information technology could advance human prospects, or as easily deliver oblivion. Even the benign momentum of extended lifespan and economic growth will provoke other hazards: an energy crisis, climate change and mass extinction.

The Earth has existed for 45 million centuries, he says. "But this is the first when one species, ours, can determine – for good or for ill – the future or the entire biosphere." Tomorrow's problems will not be solved by abandoning science, but by embracing it, and applying it for the good of all. In effect, the problems are political: science is good if people use it wisely and share its benefits. That is common sense. It stands to reason. But here is the paradox: scientists since Galileo have repeatedly overturned common sense, and shown that reason without secure knowledge is an uncertain guide. Politicians are chillingly willing to invoke common sense and reject science when it suits them. So those senators, congressmen and parliamentarians who implicitly endorse electromagnetic theory whenever they read messages on a mobile phone also feel free to dismiss climate change as uncertain or a simple conspiracy.

This really is irrational: the scientific method behind meteorology, molecular biology and quantum mechanics is the same. The past 50 years have seen a matchless growth in scientific discovery. It would be good for politics – and good for everybody – if the rest of us understood a little more not just about the results of science, but about how they were achieved.